An investigation of the block shear strength of coped beams with a welded

clip angles connection – Part I: Experimental study

Michael C. H. Yama*, Y. C. Zhongb, Angus C. C. Lamb, V. P. Iub

aDepartment of Building and Real Estate, The Hong Kong Polytechnic University, Hung Hom, Kowloon,

Hong Kong, China

bDepartment of Civil and Environmental Engineering, University of Macau, Macau, China

Abstract

The ends of a coped beam are commonly connected to the web of a girder by double

clip angles. The clip angles may either be bolted or welded to the web of the beam. One

of the potential modes for the failure of the clip angles connection is the block shear of

the beam web material. To investigate the strength and the behavior of the block shear

of coped beams with welded end connections, ten full-scale coped beam tests were

conducted. The test parameters included the aspect ratio of the clip angles, the web

shear and tension area around the clip angles, the web thickness, beam section depth,

cope length, and connection position. The test results indicated that the specimens

failed, developing either tension fractures of the web near the bottom of the clip angles

or local web buckling near the end of the cope. Although the final failure mode of the

six specimens was local web buckling, it was observed during the tests that these

specimens exhibited a significant deformation of the block shear type prior to reaching

their final failure mode. No shear fracture was observed in all of the tests. A

comparison between the ultimate loads in the test and the predictions using the current

design equations indicates that the current design standards such as the AISC-LRFD,

CSA-S16-01, Eurocode 3, BS5950-1:2000, AIJ and GB50017, are inconsistent in

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predicting the block shear strength of coped beams with welded end connections. The

analytical study of the strength of the test specimens using the finite element method, a

parametric study, and a proposed design model for designing block shears for coped

beams with welded clip angles are included in a companion paper.

Keywords: Block shear tests, Coped beams, Welded clip angles, Tension fracture, Local web

buckling

*Corresponding author: Tel. (852) 27664380; fax: (852) 27645131 Email address: bsmyam@polyu.edu.hk (Michael C. H. Yam)

1. Introduction

In steel construction, beams are often coped (cut away) at the flanges to provide

clearance for the framing beams or to maintain the same elevation for intersecting

beams. The cope can be at the top (Fig. 1), the bottom, or both flanges near the

connection in order to facilitate construction. The ends of the coped beam are

commonly connected to the web of the girder by double clip angles. The clip angles

may be either bolted or welded to the web of the coped beam. One of the potential

modes of the failure of the coped beam with a clip angles connection is the block shear

of the beam web material.

Block shear is a phenomenon of rupturing or tearing, where a block of material is

torn out by a combination of tensile and shear failure (Birkemoe and Gilmor [1]).

Figure 2 shows the potential block shear failure mode in a coped beam at the shear

connection. The web block can be partially or entirely torn out from the remaining part

of the beam. Block shear is usually associated with bolted details, because a reduced

area is present in such cases. However, block shear may also be a potential failure

mode in welded connections depending on the details of the connection. The block

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shear failure mode appears in different types of bolted structural members such as

gusset plates, coped beams, angles, or tee-sections (Hardash and Bjorhovde [2]; Epstein

[3]; Epstein and Stamberg [4], Epstein and McGinnis [5], Franchuk et al. [6], Orbison

et al. [7], etc.).

The block shear failure mode of coped beams was first identified by Birkemoe and

Gilmor [1]. In their tests, the coped beam failed by the tearing of the web as a block of

material at the shear connection. The authors suggested that the failure model of block

shear was provided by a combination of tensile and shear stresses acting over their

respective areas (across plane AA and plane BB, respectively) as shown in Fig. 3. Yura

et al. [8] conducted a series of twelve coped and uncoped beam tests with bolted double

clip angle connections. Among eight coped beam tests, three exhibited failure of the

block shear type. The specimens with two lines of bolts had a lower capacity than

desired. A further investigation by Ricles and Yura [9] was carried out to examine the

block shear failure mode of coped beams for bolted connections. The test parameters

included the end and edge distance, bolt arrangement, and the type of holes. All seven

coped beam specimens failed in the block shear mode and the web buckled at the cope

in four of them. Based on the test and the finite element analysis results, the authors

suggested assuming shear yielding for the vertical side of the web and tensile fracture

for the horizontal side (perpendicular to the applied reaction force at the coped end) in

evaluating the block shear strength of the connection. It was further noted that the shear

yielding that occurred along the gross vertical area of the web was based on the

experimental observation. This implied that the connection capacity was the sum of a

triangular normal stress on the net area of the tension face and shear yielding on the

gross shear area as shown in Fig. 4. The proposed capacity equation is as follows:

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0.5 0.6= +u nt y gvP F A F A (1)

where:

P is the ultimate connection capacity;

Fu is the tensile strength;

Fy is the yield strength;

Ant is the net tension area, and

Agv is the gross shear area.

Aalberg and Larsen [10] examined the behavior of coped I-beams with bolted end

connections fabricated from high-strength steel and normal structural steel. Identical

failure modes were observed for both normal and high-strength steels except that the

connection ductility was reduced for the high-strength steel specimens. A

comprehensive review of block shear issues was conducted by Kulak and Grondin [11],

[12]. They revisited the block shear failure mode in different cases of coped beams,

gusset plates, and angles. The review showed that the failure modes were significantly

different in two important categories, namely: gusset plates and the web of coped

beams. Taylor [13] discussed the issue of the lack of experimental data for the block

shear strength of coped beams with welded connections. Most recently, Franchuk et al.

[6], [14] conducted an extensive experimental program consisting of seventeen tests to

investigate the block shear behavior of coped beams with bolted connections. The test

results indicated that magnitudes of tension and shear areas significantly affect

connection capacity. The test results also substantiated the previous experimental

observation that shear yielding on the gross (vertical) area should be used in the block

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shear design of coped beams. The latest research was performed by Topkaya [15]. A

finite element parametric study on the block shear failure of steel tension members was

carried out to develop a block shear capacity prediction equation. The parametric study

was conducted to identify the important parameters, such as ultimate-to-yield ratio,

connection length, and boundary conditions.

Based on the above discussion, it can be seen that all of the available experimental

and analytical studies on the block shear of coped beams concentrated on bolted end

connections. Therefore, the main objective of this study is to provide experimental data

for the block shear strength and behavior of coped beams with welded clip angle

connections. The evaluation of the ultimate strength of the test specimens using current

design codes (AISC-LRFD [16], CSA-S16-01 [17], Eurcode 3 ENV 1993-1-1 [18],

BS5950-1:2000[19], AIJ [20] and GB50017 [21]) will also be presented.

2. Experimental program

2.1 Test Specimens

The purpose of the experimental program was to examine the block shear failure

strength and behavior of a coped beam web with a welded clip angles connection. A

total of ten full-scale tests were conducted in the experimental program. The test

parameters included connection geometry and cope details such as the aspect ratio of

the clip angles, the tension and shear area of the web block, web thickness, beam

section depth, cope length, and connection position. The test was conducted

individually at each end of the 3.3 m long test beam. The schematics and details of the

specimens are shown in Figs. 5, 6, and 7. These five test beams were fabricated from

three different section sizes, including universal beam UB406x140x46, UB457x191x74,

and UB356x171x67 (SCI [22]). Grade 43 steel conforming to BS 4360 [23] was used

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for the beams. All of the double clip angles were fabricated by 16 mm steel plates

conforming to BS 4360 [23] Grade 50 to provide the required connection dimensions.

The angles were designed to provide enough strength for the connections and, at the

same time, to minimize the in-plane rotational stiffness in order to simulate a simply

supported boundary condition. The double angles were welded to the web of the beams.

The nominal and measured dimensions of the beam sections and the connection

details are shown in Table 1 and Table 2, respectively. These tables should be read in

conjunction with Fig. 5. The test beams were each designated by a letter (A through E),

and each end connection was designated by a number, 1 or 2, respectively. Each

specimen was also designated according to the beam type, and the testing variable was

assigned to facilitate the identification. For example, A1-406r3 represents beam A,

connection 1, and UB406x140x46 section with an aspect ratio of around 3. Figure 6

illustrates the typical overall design dimensions of the coped beam specimens and the

clip angles, and Fig. 7 presents the connection details of all of the specimens.

As summarized in Table 3, the test parameters included the aspect ratio of the clip

angles, the tension and shear area of the web block, web thickness, beam section depth,

cope length, and connection position. Only one parameter was varied in each group of

tests. The specimens with various configurations were carefully designed to fail in the

block shear mode by the current design practice. Note that for the aspect ratio series,

the design capacities of the related tests were nearly identical for the purpose of

comparison. The top flange was coped for all specimens. In general, the cope

dimensions were fixed, with the cope depth extending 30 mm below the top flange and

the cope length extending 50 mm away from the end of the clip angles except for the

specimens that were employed to study the effect of cope length.

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In order to obtain the material properties, tension coupon tests were carried out.

Tension coupons were prepared from the web and the flange of the test beams and then

tested according to the ASTM A370 standard [24]. An extensometer with a 50 mm

gauge length was used to measure the strain in the coupon and the load was obtained as

a read-out of the testing machine. Pairs of strain gauges were mounted on both faces of

the coupons in order to determine the modulus of elasticity (E) of the steel in the elastic

range. The static readings were taken on the yield plateau, along the strain hardening

curve, and near the ultimate tensile strength.

2.2 Test setup, instrumentation, and test procedures

The test setup is shown schematically in Fig. 8. The beam specimen with welded

clip angle connections was installed to the column by 24 mm diameter bolts. Washers

were also placed between the outstanding leg of the angles and the supporting column

in all tests to minimize the end rotational stiffness. The bolts were then tightened to a

snug-tight condition. Load was applied to the beam vertically by a 890 kN hydraulic

cylinder. The load position was chosen to produce block shear failure in the connection

and to avoid either shear or bending failure of the test beam. The chosen load position

also has little effect on the stress distribution in the coped region. The distance, L, from

the load position to the reaction end was 510 mm (1.3D), 600 mm (1.3D), and 550mm

(1.5D) for the test beams Beam406, Beam457, and Beam356, respectively, as

illustrated in Fig. 8.

Roller assemblies were used at the load position and the support so that both

rotation and longitudinal movements were allowed. Lateral bracings were provided at

the load position and the support to prevent lateral movements of the test beam.

Additional lateral bracings were provided at the top flange of the beam near the cope

end to improve the lateral stability of the connection. Stiffeners were welded on both

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sides of the web at the load position in order to avoid local web crippling. Load cells

were used to record the applied load and the support reaction.

Linear variable differential transformers (LVDT) were employed to measure the

displacements. The locations of the LVDTs are typically shown in Fig. 9. To measure

the main features, LVDTs were placed separately at the bottom of the beam underneath

the load point, and at the top and the bottom of the beam at the connection. The

displacement of the clip angle at the column was also recorded. The overall deflection

was determined by taking the difference between the displacement under the applied

load and the displacement of the clip angles, which excluded the displacements due to

bolt bearing and slippage. In addition, the deformation between the vertical

displacements measured from below and above the connection provided a good

indication of the significant tensile yielding or sudden fracture of the beam web.

Another LVDT was set at the top flange near the loading position to detect lateral

movements. The rotation of the angles and the tested beam end were also recorded by

LVDTs. In addition, an inclinometer was mounted on the web at the centroid of coped

section to monitor end rotation. Longitudinal strain gauges and rosettes were

extensively mounted around the connection to measure the strain distribution at the

critical area, as shown in Fig. 10. More details regarding the instrumentation can be

found in Zhong et al. (2004). All readings were collected by a data acquisition system.

Before the test, the specimen was whitewashed to make it possible to detect the

yielding process, and 50 mm square grid lines were drawn to show the web

deformations.

In general, the test procedures were similar for all of the specimens. The loading

process was divided into two stages: load control in the beginning and stroke control

when nonlinear behavior commenced. Load was applied incrementally and a smaller

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load increment was used to capture the nonlinear behavior in the inelastic stage of the

tests. During the test, it was necessary to hold the loading at regular intervals for static

equilibrium so that the specimens could redistribute the stress and deform completely,

therefore making it possible to obtain the reading on static load. Readings of load cells,

strain gauges, and LVDTs were taken continually during the loading process. The

yielding pattern and process were recorded in detail. The test was terminated when the

maximum load was reached and the load decreased significantly. After the test on one

end was completed, the other end of the beam was installed to the column, and a new

test was then conducted.

3. Test results

3.1 Material test results

The tension coupon test results for all specimens are summarized in Table 4, and

the results for clip angles are included as well. Since the block shear failure was mostly

associated with the beam web, the mean values of the coupons from the web of test

beams were used as the basic material properties for the specimens. The average static

yield strength for the specimens ranged from 304.1 MPa to 371.6 MPa, whereas the

average static ultimate strength ranged from 442.2 MPa to 487.7 MPa. Although Grade

50 steel was assumed in the design of the clip angles, it was believed that Grade 43

steel was used instead for the clip angles based on the tension coupon test results as

illustrated in Table 4. The material properties for S275 and S335 (EN10025 -2:2004)

are also included in the table for comparison purpose.

3.2 General

The test results are summarized in Table 5, where the static values of the ultimate

load are reported, and the connection reactions and moments were calculated from

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static equilibrium. For simplicity, only the letter and the first number in the specimen

designation were used to identify the specimens (for example, specimen A1 instead of

specimen A1-406r3). The moment developed in the connection was found to be small

compared with the yield moment of the beam. In general, there were two kinds of

failure modes in the tests: the block shear of the beam web with tension fractures

underneath the clip angles and local web buckling near the end of the cope. Two

specimens failed in the block shear mode while six specimens ultimately failed in local

web buckling near the cope due to combined shear and bending. Although the final

failure mode of the six specimens was web local buckling, it was observed during the

tests that these specimens exhibited a significant block shear type deformation prior to

reaching their final failure mode. In the block shear cases, necking of the tension area

in the web underneath the clip angles was observed before the web fractured abruptly.

The reduction in web thickness in the tension region is also included in Table 5. A

tensile crack developed in the web along the bottom of the welded clip angles rather

than a complete web block tear-out. No signs of shear fracture along the vertical plane

were observed. As to the remaining two specimens, the test loads exceeded the capacity

of the testing frame; hence, these two tests were terminated at the safe load of the test

setup.

The photographs of typical failed specimens at the ultimate stage are shown in Fig.

11. Figure 12 contains an illustration of typical local web buckling failure near the cope

end. In general, a similar yielding pattern was observed for the specimens. Yield lines

were usually initiated in the web either underneath the welded clip angles at the

extreme beam end or near the cope end. Eventually, the yield lines extended through

the web block and could be obviously observed below the welded clip angle and across

the cope end. These yield lines indicated that significant deformation had occurred in

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these regions. Yield lines could also be found in the shear area near the welded clip

angles in most cases.

The results showed that the web plate buckled to various extents at the cope end

even though the flange near the cope was braced against lateral movement. Severe

compression and shear yielding was observed near the cope end before the specimens

reached the ultimate loads. This indicated that local web buckling was also a potential

failure mode for coped beams with welded clip angle connections. This failure mode

was also observed by Ricles and Yura [9] in their coped beam tests. They pointed out

that the high horizontal compressive stresses in the web could cause the web to buckle

at the cope.

3.3 Load deflection behavior

A typical applied load versus deflection curves are shown in Fig. 13. Plotted on the

horizontal axis is the net deflection at the load point, which was determined by taking

the difference between the displacement under the applied load and the displacement of

the clip angles; hence, this net deflection excluded the displacements due to bolt

bearing and slippage. Thus, the overall behavior of the test beams can be presented.

Generally, similar behavior was observed of the specimens with regard to the two kinds

of failure modes. As the load was applied, yielding first appeared in the web

underneath the welded clip angles or near the cope end. Nonlinear behavior then

commenced. When the load continued to increase, shear yielding developed gradually

along the vertical area near the welded angles. High flexural stresses in the upper

region of the web increased and excessive deformation developed. The web block

deformed significantly before the web plate near the cope end became distorted or

buckled inelastically. Subsequently, for specimens C2 and E1, tension fractures

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developed abruptly underneath the clip angles, and the load therefore decreased

significantly. Continued loading caused further opening of the cracks. As to specimens

A1, A2, B1, B2, D1, and E2, at the ultimate load level severe compression as well as

shearing caused local web buckling at the cope end, and the load subsequently

descended.

3.4 Strain distribution

Strain distributions are presented in the critical area along the web block as

indicated by the locations of strain gauges and rosettes shown in the insets of Figs. 14

and 15. The strain distributions are plotted within the elastic stage, against the same

load levels of 70 kN and 183 kN. Only the strain distributions for specimen E1 are

presented since there is no significant difference in the strain distributions of other

specimens. The vertical longitudinal strain distribution along the horizontal plane

underneath the welded clip angles (the tension area) for specimen E1 is plotted in Fig.

14. As expected, the strain was largest at the beam end and decreased along the length

of the tension area. An almost linear strain distribution was found within the elastic

range. This kind of distribution reflected the load eccentricity on the connection that

caused the rotation of the web block. The line of action of the vertical reaction force at

the beam end was outside the centroid of the web block and consequently induced this

eccentricity. However, at same load level, the positions of the neutral axis for the

longitudinal strains were close to each other for specimens with the same beam sizes.

For the cases with a large area of tension, the longitudinal strains beneath the corner of

the clip angle indicated slight compression at the beginning of loading. It was believed

that the compressive strain would shift to tension as the load increased.

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Vertical shear strain distributions along the vertical plane near the welded clip

angles (the shear area) are also examined. Typically, the result for specimen E1 is

shown in Fig. 15, in which the dash line indicates the shape of the clip angle. It can be

seen from the figure that the shear stress distribution determined by three rosettes was

uneven. It differed from the shear distribution calculated by the shear formula for the

reduced beam section. The stress concentration around the top and the bottom corners

of the clip angle was believed to have some influence on the reading on strains

measured at these positions. In general, the shear strain distributions of the other

specimens were similar. Since the number of rosettes in the shear area was limited, the

shear strain profile obtained might not represent the entire shear strain distribution in

this area for the test specimen. Nevertheless, the shear strain values measured at the

critical locations provide the data for the calibration of the finite element model. It will

be seen that the measured shear strains are consistent with the numerical ones. The

calibration and discussion of the stress/strain distribution of the finite element model of

the test specimens can be found Yam et al. [25] and Zhong [26].

The local bending effect around the web block was caused by the connection

rotation. The distribution of flexural strains in the shear area can be illustrated by the

longitudinal strains in the horizontal direction (marked with No. 7, 10, and 13 in the

inset of Fig. 16). The distribution features are similar among all specimens. Take for

example specimen E1 as shown in Fig. 16. High flexural compressive strains

developed in the beam web near the cope, while tensile strains developed near the

bottom of the clip angle. It was believed that the high compression as well as the

shearing that developed in the compression region would cause early yielding of the

web plate; and that, consequently, at a high load significant yielding would induce

inelastic web buckling at the cope end.

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4. Discussion of the test results

4.1 Failure mode

Previous studies focused on the block shear failure of coped beam web with bolted

connections. For bolted end connections, a reduction in the cross-sectional area due to

the presence of holes has adverse effects on the strength of the connections. The

concentration of stress at the bolt holes initiated fracturing, and contributed to the block

shear failure mode. For welded end connections, since there is no reduction in gross

section area due to bolt holes, the behavior and failure mode of the connection would

be different.

As described before, two kinds of failure modes were observed in the tests, namely;

block shear failure and local web buckling at the cope end. Block shear failure was

exhibited in a partial tear-out of the web block with a tension fracture underneath the

clip angles. The tension fracture was triggered at the extreme end of the beam web, and

necking of the web plate was observed before a sudden rupture. Shear yielding rather

than shear fracture was observed along the vertical plane of the shear area. Shear

ultimate strength was difficult to achieve since the shear deformation was relatively

small compared with the tension deformation. Hence, tension fracture was reached

prior to shear fracture due to the significant deformation in the area of tension. Another

potential failure mode was local web buckling near the end of the cope. High

compressive stresses and shear stresses were localized in the web near the cope because

of the combination of bending and shear in the reduced section; hence resulting in

extensive yielding and consequently inducing local web buckling in that region.

As mentioned before, lateral bracing at the top flange near the cope was provided to

improve the lateral stability of the test beams. However, various degrees of web

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buckling were still observed in most cases, and six specimens among them ultimately

failed in the local web buckling mode. In fact, in previous studies, such as those by

Birkemoe and Gilmor [1] and Ricles and Yura [9], local web buckling was also

observed in cope beam tests for block shear with bolted connections. For those

specimens that failed due to local web buckling, excessive deformation developed

around the web block at a high load due to significant yielding in the tension and shear

areas. However, the deformation was insufficient to induce fracturing even though the

ultimate tensile stress was attained in the area of tension. On the other hand, severe

compression and shear yielding accumulated near the cope end, thus eventually

resulting in local web buckling. Nevertheless, observations showed that these

specimens exhibited a deformation of the block shear type prior to reaching their

ultimate loads with local web buckling failure.

4.2 Effect of aspect ratio

Aspect ratio has been defined as the ratio of vertical shear area (b’) to the horizontal

tension area (a) of the web block, as indicated in Fig. 5. Note that the design capacities

of the related specimens are nearly identical for the purpose of comparison. The aspect

ratio was examined in two series of tests. In the first series, specimens A1, A2, and B2

had an aspect ratio of 3.6, 2.3, and 1.4, respectively. Their final failure mode was local

web buckling, as shown in Table 5. For specimens A2 and B2, the aspect ratio varied

from 2.3 to 1.4 while the capacity of A2 was 12% higher than that of B2. Although

specimen A1 had the largest aspect ratio, it was worth noting that the double clip angles

used in this specimen was different from those of the other specimens due to a

fabrication error. This had an adverse effect on the capacity of the specimen. Since the

bolted leg of the clip angle was fabricated shorter for the arrangement of the bolts, the

boundary condition of the pin support that was simulated by the clip angle was

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influenced to some extent. This meant that the position of the pin support for the beam

specimen was therefore lowered, while the rotational stiffness of the joint was reduced.

Since the negative moment that developed in the connection at the beam end was due

to a slight fixity in connection, the negative moment of A1 in the connection was

smaller than that of A2 and B2, as shown in Table 5. Hence, it was believed that the

reduction in the capacity of specimen A1, which failed because of the local web

buckling, was attributable to the influence of the clip angle. The results of the finite

element analyses that will be discussed in the companion paper (Yam et al. [25]) also

indicates that specimen A1 would have a larger capacity than specimen A2 by using

double clip angles similar to those of the others. For specimens C1 and D1 in the

second series, the aspect ratio was 3.8 and 1.6, respectively. Although the ultimate

failure of C1 did not occur before the test was terminated at the safe load of the test

setup, it was believed that C1 would have a much larger capacity than D1 from the

trend of the load deflection curve, which can be observed in Fig. 17.

In addition, further observations of the yield lines also led to an interpretation of the

effect of the aspect ratio on the deformation of the web. For specimen D1, many yield

lines were observed in the beam web near the bottom of the clip angle as shown in Fig.

11d. This might indicate that the web material in this region had been subjected to

excessive deformation caused by local bending due to the connection rotation. On the

other hand, for specimen C1, there were significantly fewer yield lines, as shown in Fig.

11b. Nevertheless, it can be seen that as the aspect ratio decreased, local bending of the

web near the clip angle due to the connection rotation was more significant. In fact, the

local bending would cause high compressive stress to the web material near the end of

the cope corner and hence might lead to a failure in the local buckling of the web. In

addition, the local bending also induced high tensile stress in the web near the bottom

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edge of the clip angle, which might initiate fractures of the web block similar to those

seen in specimens C2 and E1.

Based on the above discussion, it is believed that the block shear capacity of the

connection decreased as the aspect ratio decreased. As the aspect ratio decreased

(increase in a), the loading eccentricity between the welded clip angle and the support

(bolted end) at the column face increased, hence generating more local bending of the

web in the vicinity of the clip angle. Since the aspect ratio is associated with the ratio of

the shear area and the tension area, it is necessary to examine these two aspects

individually to reveal their relationship and the effect on the strength of the connection.

4.3 Effect of shear area and tension area

Specimens C1 and C2 were identical in all aspects except for the shear area. The

length of the shear area (b) of specimen C1 and C2 was 170 mm and 120 mm,

respectively. As shown in Fig. 18, the connection stiffness of C1 was higher than that

of C2. Specimen C2 failed due to block shear with tension fractures. However, the

strength of C1 exceeded the test setup capacity, so it was certainly larger than that of

C2. According to the test data, C1 was estimated to be at least 10% larger in capacity

than C2. As expected, the connection capacity was improved by increasing shear area.

For specimens C2 and D1, the length of the tension area (a) varied from 50 mm to

90 mm, while the shear area of the specimens was held at a constant value of 120 mm

in length. As shown in Table 5, the capacities of these two specimens were very close,

even though there was a significant difference in the tension area. Observed during

these two tests, the webs buckled similarly before their final failure. However,

specimen C2 eventually failed due to block shear with tension fractures, while

specimen D1 failed due to local web buckling. The yielding pattern of specimen D1

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showed that there was excessive deformation in the web around the clip angle caused

by significant connection rotation. The rotation was believed to have been produced by

the eccentricity of the reaction force on the web block, while the eccentricity was

associated with the area of tension. Hence, this indicated that increasing the area of

tension led to an increase in loading eccentricity and therefore generated more bending

stress to the edge of the beam web region near the clip angles and the cope end. This

increase in bending stress counteracted the increase in the connection strength due to

the additional area of tension and initiated either the earlier local web buckling in the

end of the cope or web tension fractures near the bottom of the clip angles. Therefore,

the capacity of specimen D1 did not increase considerably even though the area of

tension increased by 80%.

4.4 Effect of web thickness

Specimens B1, C2, and E1 were fabricated from three different beam sections with

identical connection dimensions. The nominal beam web thickness (tw) was 6.8 mm for

specimen B1, and 9.1 mm for specimens C2 and E1. As shown in Table 5, when the

web thickness of the specimens decreased the ultimate loads decreased; however, the

decrease was not directly proportional to the change in the thickness of the web. This is

illustrated in Fig. 19, where the original reaction versus web deformation curve of

specimen B1 was modified proportionally by multiplying a scale factor (9.1/6.8) to

account for the difference in thickness from the original one. It can be seen from this

figure that the modified ultimate load of specimen B1 (527 kN) was 14% less than that

of specimen E1 (601 kN), even though the two specimens had a similar ultimate tensile

strength (Fu). The figure also shows that the behavior of specimens C2 and E1, which

had the same web thickness, was nearly identical. For thin web specimen B1, its weak

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axis flexural stiffness was lower than that of the other two specimens and therefore

increased the susceptibility of the beam web to local buckling. Subsequently, like

specimens C2 and E1, B1 ultimately buckled rather than failed by block shear with

tension fractures.

4.5 Effect of Beam Section Depth

The effect of beam section depth can also be observed in Fig. 19. For specimens C2

and E1, the web thicknesses and the dimensions of the connections were identical while

the depth of the beam section varied from 457 mm to 363 mm. The results showed that

these two specimens had almost the same amount of connection ductility. Specimen C2,

with a section depth that was 26% deeper, only produced a 5% increase in capacity

regardless of the slight difference in the material tensile strength. In addition, the

failure modes (tension fractures) of these two specimens were similar, implying that

block shear capacity was not affected by section depth.

4.6 Effect of Cope Length

The cope length (c) varied from 150 mm to 80 mm for specimens D1 and D2,

respectively, and the other details for these two specimens were identical. Specimen D2

had the smallest cope length of all of the specimens, in which the uncoped top flange

extended close to the end of the beam and beyond the region of the shear path near the

welded clip angle. As shown in Fig. 20, it can be seen from the comparison of

specimens D1 and D2 that cope length had a significant effect on connection capacity.

Connection D2 was much stiffer than D1. The web plate did not buckle and only a

small deformation was observed in specimen D2 at the maximum load of the test frame.

Therefore, the capacity of D2 was certainly larger than that of D1. Hence, for the

specimen with a shorter cope length the connection was strengthened by the uncoped

20

top flange; the susceptibility to local web buckling near the cope end was therefore

reduced. In other words, increasing the cope length increased the possibility of

instability and therefore led to a decrease in the connection capacity.

4.7 Effect of Connection Position

For specimens E1 and E2, the connected position (p) of the welded clip angles

varied from 20 mm to 45 mm (the vertical distance from the clip angle to the top edge

of the beam web as shown in Fig. 5) while other details were identical. Similar load

deflection behavior and a slight difference in capacity were observed between these

two cases. The capacity of E2 was 3% less than that of E1, even if the vertical shear

path (b’) of E2 was longer. In addition, E2 ultimately failed in local web buckling

mode rather than in the block shear with tension fractures as E1 did. This may indicate

that the final failure mode of the specimen was affected by the connected position of

the welded clip angles. Since high compressive and shear stresses developed in the

beam web between the top of the clip angle and the cope end, it was believed that a

local web buckling failure would likely occur in the case where the clip angles was

placed at a lower position.

5. Comparison of Test Results with Current Design Methods

5.1 General

The block shear design equations prescribed by the current standards of CSA-S16-

01 [17], AISC LRFD [16], Eurocode 3 ENV 1993-1-1 [18], BS 5950-1:2000 [19], AIJ

[20] and GB50017 [21] were used to evaluate the block shear strength of the test

specimens. However, it should be noted that the block shear design equations for coped

beams were mainly associated with bolted end connections. The failure mechanism in

welded end connections may be different from that of bolted end connections since, in

21

the former, there is no reduction in gross section area due to bolt holes. Nevertheless,

these equations are also used for welded end connections. Consequently, for the test

specimens in this study, the block shear failure was checked around the periphery of

the welded connections. As mentioned above, although the final failure mode of six

specimens was local web buckling, it was observed during the tests that these

specimens exhibited a significant deformation of the block shear type prior to reaching

their final failure mode. Therefore, it is believed that the use of the block shear design

equations for the specimens that failed in local web buckling would provide an

indication of the strength of the connection.

5.2 Current Design Standards

5.2.1 CSA-S16-01 (2001)

The CSA-S16-01 [17] standard provides two equations (Eq. (2) and Eq. (3)) to

evaluate the block shear strength of connections.

(0.5 0.6 )= +r u nt y gvP F A F Aφ (2)

(0.5 0.6 )= +r u nt u nvP F A F Aφ (3)

where:

Pr is the factored ultimate connection capacity;

φ is the resistance factor;

Fu is the tensile strength;

Fy is the yield strength;

Ant is the net tension area;

Agv is the gross shear area; and

22

Anv is the net shear area.

As suggested by Kulak and Grondin [12], the contribution of the area of tension is

reduced by one-half, which implies that a triangular stress block with a maximum stress

of Fu is assumed. Equation (2) assumes that the block shear capacity is determined by a

non-uniform stress distribution with an average stress of 0.5Fu at a net area of tension,

along with the shear yielding stress at the gross shear area; while Eq. (3) assumes that

the shear contribution is the shear rupture at the net shear area. The lesser of above two

equations should be used as the block shear capacity. A comparison of the previous

test data on coped beams with bolted end connections shows that this procedure

provides conservative results with an average test-to-predicted ratio of 1.20. In the

current study, since no shear fracture was observed for the failed specimens in this

study, only Eq. (2) (the lesser one) was used to evaluate the block shear strength of the

test specimens. Without the reduction in bolt holes when calculating area, the gross

area and the net area in Eq. (2) were identical.

5.2.2 AISC LRFD (1999)

For the AISC LRFD [16] standard, again, two equations (Eq. (4) and Eq. (5)) are

provided:

If 0.6≥u nt u nvF A F A :

( 0.6 ) ( 0.6 )= + ≤ +r u nt y gv u nt u nvP F A F A F A F Aφ φ (4)

If 0.6<u nt u nvF A F A :

( 0.6 ) ( 0.6 )= + ≤ +r y gt u nv u nt u nvP F A F A F A F Aφ φ (5)

23

where:

Agt is the gross tension area and the other symbols have been defined above.

When the ultimate rupture strength at the net section is used on one segment,

yielding at the gross section shall be used on the perpendicular segment. The design

equations incorporate two possible modes of failures: the rupturing of the net tension

area combined with yielding of the gross shear area, or yielding of the gross tension

area combined with rupture of the net shear area. The upper limit is the sum of tension

rupture on the net tension area and shear rupture on the net shear area. It should be

noted that the first failure model is reasonable and supported by test observations.

Experimental results in which block shear is evident tend to exhibit a failure mode

similar to that described by Eq. (4); however, the qualifying condition listed in the

specification makes it rarely control the design. Thus, Eq. (5) will commonly govern in

practice.

Kulak and Grondin [12] points out that the possibility of attaining the shear

ultimate strength in combination with the tension yield strength seems unlikely due to

the small ductility in tension as compared with shear, and there is insufficient tensile

ductility to permit the occurrence of shear fractures. Nevertheless, the use of Eq. (4)

and Eq. (5) does not provide good predictions of the available test results and produces

a high degree of variation. In particular, for the two-line bolted connections, the

equations are for the most part not conservative. In general, they do not accurately

represent the failure modes observed in tests. The AISC LRFD specification [16] also

indicates that the block shear failure mode should also be checked around the periphery

of welded connections. For the current study, the larger one of Eq. (4) and Eq. (5) was

used to evaluate the block shear strength of the test specimens.

24

5.2.3 Eurocode 3 ENV 1993-1-1

For Eurocode 3 [18], a single equation can be derived from a series of equations

according to the specifications for block shear on coped beams as follows:

0

1 1 1( )3 3

⎡ ⎤= − +⎢ ⎥⎣ ⎦r u gt ot w y gv

M

P F L kd t F Aγ

, (6)

where:

0Mγ is the partial safety factor for resistance (a vale of 1.0 is used in this study);

Lgt is the length of the gross tension area;

dot is the hole size for tension area; and

k is the coefficient for tension area as follows:

for a single line of bolts: 0.5=k ;

for two lines of bolts: 2.5=k .

The equation combines the reduced normal stress acting over the tension area with

shear yielding acting over the gross shear area. Franchuk et al. [6] indicated that the

reduction coefficient of 13

for the normal stress is considered similar to the 0.5 used

in CSA-S16-01, although this value appears to be derived from the von Mises yield

criterion. It is found that the equation provides a very conservative prediction even for

two-line bolted connections.

5.2.4 BS 5950-1:2000

In this updated BS 5950-1:2000 standard [19], block shear for bolted connections is

covered as follows:

25

0.6 ( ) 0.6y e t t w y v wP p K L kD t p L t= − + , (7)

where:

P is the ultimate connection capacity

yp is the design strength

Ke is the effective net area coefficient

t is the web thickness

Lt is the length of the tension area

Lv is the length of the shear area

k is defined above, and

Dt is the hole size for the tension area

For general purposes regardless of steel grade, 1.2

se

y

UKp

= , where Us is the minimum

tensile strength. Therefore, Eq. (7) becomes:

0.5 ( ) 0.6s t t w y gvP U L kD t p A= − + (8)

Disregarding the partial factor and the different definitions for design strength, this

equation is very similar to that of Eurocode 3, except that 0.5 instead of 13

is used

again for the reduction of the tension contribution. Compared with Eq. (2), there is a

slight difference in the calculation of the net tension area. Equation (8) is believed to

produce conservative results for two-line bolted connections in coped beams.

For welded end connection, if the design strength and the minimum tensile strength

in Eq. (8) is substituted by Fy and Fu respectively, an equation the same as Eq. (2) can

be deduced. This means that for a welded end connection, the prediction by BS 5950-

26

1:2000 [19] is exactly identical to that provided by the CSA-S16-01 standard [17].

Thus, the evaluation results for BS 5950-1:2000 [19] will not be repeated here.

5.2.5 Standard for limit state design of structures (AIJ 1990), Architectural Institute

of Japan,

The AIJ (1990) [20] provides the following conservative procedure:

1( )3

= +r u nt y nvP F A F Aφ (9)

1( )3

= +r y nt u nvP F A F Aφ (10)

where the symbols are similar to the ones defined before. The lesser of the equations is

used for the connection capacity. It combines tensile and shear stresses acting on both

net areas. The results show that these equations give more conservative predictions, but

with a high degree of variation. In addition, these equations cannot represent the actual

failure mechanism for block shear in coped beams.

In contrast with the equations of AISC LRFD [19] (Eq. (4) and Eq. (5)), there is

only a negligible difference in the coefficient. In fact, the AISC LRFD standard [19]

uses the larger of these two equations instead of the smaller.

5.2.6 Chinese Standard GB50017 (2003)

Based on the results of the gusset plates test, a block shear equation is derived and

added to the latest version of the Chinese standard for the design of steel structures

(GB50017-2003 [21]). From the commentary in the code, the following explicit

equation can be derived for coped beams:

27

13u nt u nvP F A F A= + , (11)

where the symbols are similar to the ones defined before. This equation assumes that

tensile rupture on the net tension area and shear rupture on the net shear area appear

simultaneously. The average test-to-predicted ratio for Eq. (11) on the results of the

gusset plates test provided in the code GB50017 [21] is 1.14. The code also shows that

the equation is applicable for both bolted and welded connections. It is interesting to

note, neglecting the partial factor, that this model is almost the same as that of the

former Canadian standard CAN/CSA-S16.1-94 [17], which is expressed as:

0.85 ( 0.6 )= +r u nt u nvP F A F Aφ (12)

5.3 Design Strength of Test Specimens Based on Current Design Standards

The ultimate strengths of the test specimens were compared to those predicted by

all of the above design equations from different design standards for block shear. The

results are summarized in Table 6. The predicted capacities were based on the

measured dimensions of the specimens, including the measured weld sizes and the

measured material properties. All resistance factors are taken as 1.0. The test-to-

predicted ratio (or termed professional ratio) of those failed specimens are listed in

Table 6.

As described before, for the six specimens that ultimately failed due to local

buckling of the web rather than block shear, the observation from test results showed

that the deformed block did appear prior to ultimate buckling of the web. Therefore,

qualitative comparisons of these specimens may still be made using the current design

28

standards. For the specimens that failed by block shear with tension fracture, the

average test-to-predicted ratios were 1.49 and 1.06 based on CSA-S16-01 [17] and

AISC LRFD [16], respectively. This may indicate that the CSA-S16-01 [17] design

model may be too conservative for block shear in coped beams with a welded clip

angles connection. At the same time, it is important to note that the average test-to-

predicted ratios for those specimens that failed due to local buckling of the web were

1.26 and 0.88, as estimated by the CSA-S16-01 [17] and the AISC LRFD [16] block

shear equations, respectively. Although the test results were not conclusive, it is

believed that current North American design standards are inconsistent to allow

predictions of the block shear of coped beams with welded end connections.

The approach of Eurocode 3 [18] produced very similar results in capacity

predictions as compared to CSA-S16-01 [17]. It was found that the capacity predicted

by Eurocode 3 [18] was about 3% larger than that of CSA-S16-01 [17], which could be

attributed to the slightly different coefficients used in the related equations. The

average test-to-predicted ratios were 1.45 and 1.22 for the block shear cases and the

local web buckling cases, respectively. Besides, as mentioned before, predictions by

BS 5950-1:2000 [19] were exactly identical to those by the CSA-S16-01 standard [17].

Consequently, it can be concluded that, in general, the current European and British

design standards are also conservative for block shear in coped beams with a welded

clip angles connection.

AIJ standard [20] did not provide a consistent prediction for both failure modes,

and generally overestimated the capacity of the specimens that failed due to local

buckling of the web. The average test-to-predicted ratios were 1.15 and 0.96 for the

block shear cases and the local web buckling cases, respectively. Nevertheless, the AIJ

standard [20] provides a safer estimation than AISC LRFD [16] because the former

29

adopts the smaller value of the two equations, while the latter uses the larger one.

However, the procedures of both the AIJ standard [20] and AISC LRFD [16] could not

accurately represent the actual failure modes observed in the tests, since no fractures

were found in the shear area.

It should be pointed out that GB50017 [21] overestimated the capacities of all

specimens. The average test-to-predicted ratios were 0.96 and 0.80 for the block shear

cases and the local web buckling cases, respectively. Hence, this standard produced

non-conservative estimates for the block shear strength of coped beams with a welded

clip angles connection. In addition, it was unlikely that the ultimate tensile strength of

the tension area and the ultimate shear strength of the shear area would be achieved

simultaneously; hence, the model did not reflect the actual failure mechanism.

Generally, the predictions using these design equations exhibited a vast degree of

variation with regard to the test data. For example, these methods often produced large

overestimations for specimens with large areas of tension, such as specimens B2 and

D1. Furthermore, in all cases, the predictions were less conservative for the specimens

that failed due to local buckling of the web, even though a significant deformation of

the block shear type occurred before the specimens reached their final failure mode.

Therefore, it is concluded that the existing design standards are inconsistent in

predicting the bock shear of cope beams with welded end connections.

6. Summary and Conclusions

To investigate the block shear strength and behavior of coped beams with welded

end connections, ten full-scale coped beam tests were conducted. The failure

mechanism in coped beams with welded end connections was different from that with

bolted end connections, since there was no reduction in the web section area due to bolt

30

holes. The test results showed that only two of the ten specimens failed by block shear

mode with tension fractures. Tension fractures occurred abruptly in the beam web

underneath the clip angles. No shear fractures were observed and no tear-out type of

block shear occurred. Local web buckling was also a potential failure mode for coped

beams with welded end connections. High compressive stresses and shear stresses were

localized in the web near the end of the cope due to the combination of bending and

shear in the reduced section, hence resulting in extensive yielding at the cope and

inducing local web buckling. However, these specimens exhibited significant

deformation of the block shear type prior to reaching their final failure mode.

The test parameters examined included the aspect ratio of the clip angles, the

tension and shear area of the web block, web thickness, beam section depth, cope

length, and connection position. The results showed that the connection capacity

increased as aspect ratio and shear area increased. A large area of tension would

increase the loading eccentricity and hence generate more bending moments to the edge

of the beam web region near the angle. A thin beam web and long cope length

increased the susceptibility to local web buckling. The depth of the beam section and

connected position did not greatly affect the connection capacity.

The design equations from current standards were used to evaluate the capacity of

the specimens. It was found that the existing design standards did not provide

consistent predictions of the block shear strength of coped beams with welded end

connections. In addition, the rules provided by the standards could not accurately

reflect the failure mode observed in the tests. For a better understanding of the

connection behavior and the failure mechanism, non-linear finite element analyses

(FEA) were carried out and presented in a companion paper (Yam et al. 2005), which

31

included a parametric study and a proposed design equation for the block shear strength

of coped beams with welded clip angles connections.

7. Acknowledgments

The authors would like to express their gratitude to the Research Committee of

the University of Macau for providing financial support for this project. The assistance

of the technical staff of the Structural Laboratory at the University of Macau, Macau,

China, is also acknowledged.

8. References

[1] Birkemoe, PC, and Gilmor, MI. “Behavior of bearing critical double-angle beam

connections,” Engineering Journal, AISC, 1978; Vol. 15, No. 4, pp. 109-115.

[2] Hardash, S, and Bjorhovde R. “New design criteria for gusset plates in tension,”

Engineering journal, AISC, 1985; Vol. 22, No. 2, second quarter.

[3] Epstein, HI. “An experimental study of block shear failure of angles in tension,”

Engineering journal, AISC 1992; Vol. 29, No. 2, second quarter.

[4] Epstein, HI, and Stamberg, H. “Block shear and net section capacities of structural

tees in tension: Test results and code implications,” Engineering Journal, 2002; Vol. 39,

No. 4, Fourth Quarter, pp. 228-239.

[5] Epstein, HI, and McGinnis, MJ. “Finite element modeling of block shear in

structural tees,” Computers and Structures 2000; Vol. 77, No. 5, pp. 571-582.

32

[6] Franchuk, CR, Driver, RG, and Grondin, GY. “Experimental investigation of block

shear failure in coped steel beams,” Canadian Journal of Civil Engineering, 2003; Vol.

30, No. 5, pp. 871-881.

[7] Orbison, JG, Wagner, ME, and Fritz, WP. “Tension plane behavior in single-row

bolted connections subject to block shear,” Journal of Constructional Steel Research,

1999; 49:225-239.

[8] Yura, JA, Birkemoe, PC, and Ricles, JM. “Beam web shear connections: an

experimental study,” Journal of the Structural Division, 1982; ASCE, Vol. 108, No.

ST2 , pp. 311-325.

[9] Ricles, JM, and Yura, JA. “Strength of double-row bolted-web connections,”

Journal of Structural Engineering, 1983; ASCE, Vol. 109, No. 12, pp.126-142.

[10] Aalberg, A. and Larsen, PK. “Strength and ductility of bolted connections in

normal and high strength steels,” In Proceedings of the Seventh International

Symposium on Structural Failure and Plasticity, Melbourne, Australia, 2000.

[11] Kulak, GL, and Grondin, GY. “Block shear failure in steel members – a review of

design practice,” In Proceedings of Fourth International workshop on Connections in

Steel Structures IV: Steel Connections in the New Millennium, Roanoke, Va., 22–25

October 2000. Edited by Leon, RT, and Easterling, WS., AISC, Chicago, Ill. pp. 329-

339, 2000.

[12] Kulak, GL, and Grondin, GY. “AISC LRFD rules for block shear in bolted

connections – a review,” Engineering Journal, AISC, 2001, 38(4): 199–203. See also

“Errata and Addendum,” Engineering Journal, AISC, 39(2).

33

[13] Taylor, JC. “More work is required,” In Proceedings of Fourth International

workshop on Connections in Steel Structures IV: Steel Connections in the New

Millennium, Roanoke, Va, Edited by Leon , R T, and Easterling, WS., AISC, Chicago,

Ill. pp 33-40, 2000.

[14] Franchuk, CR, Driver, RG, and Grondin, GY. “Block shear failure of coped steel

beams,” Proceedings of 4th Structural Specialty Conference of the Canadian Society

for Civil Engineering, Montreal, Quebec, Canada, 2002.

[15] Topkaya, C. “A finite element parametric study on block shear failure of steel

tension members,” Journal of Constructional Steel Research, 2004; Vol. 60, Issue 11,

pp. 1615-1635

[16] American Institute of Steel Construction (AISC). Load and resistance factor

design specification for structural steel buildings, Chicago, IL, USA, 1999.

[17] Canadian Standards Association. (CSA). CAN/CSA-S16-01 Limit states design of

steel structures. CSA, Toronto, ON, Canada, 2001.

[18] European Committee for Standardisation (ECS) (1992). Eurocode 3: design of

steel structures – Part 1.1: general rules and rules for buildings. ENV 1993-1-1,

Brussels, Belgium, 1992.

[19] British Standards Institution (BSI) BS 5950: Structural use of steelwork in

building – Part 1: Code of practice for design –rolled and welded sections, 2001.

[20] Architectural Institute of Japan (AIJ). Standard for limit state design of steel

structures, 1990.

[21] Ministry of Construction of PR China (2003). Code for design of steel structures

(GB50017–2003), Chinese Planning Press., Beijing, China, 2003 (in Chinese).

34

[22] Steel Construction Institute, Steelwork design guide to BS5950: Part 1:1990.

Volume 1: Section properties, member capacities, 4th edition, 1997.

[23] British Standards Institution (BSI) (1990). BS 4360: Specifications for weldable

structural steels, London. 1990.

[24] American Society for Testing and Materials (ASTM). Standard test methods and

definitions for mechanical testing of steel products, ASTM Standard A370-02,

Philadelphia, Pa, 2002.

[25] Yam, CHM, Zhong, YCJ, Lam, CCA, and Iu, VP. “ An investigation of the block

shear strength of coped beams with a welded clip angles connection, Part II: Analytical

Study,” Journal of Constructional Steel Research (companion paper).

[26] Zhong, YCJ. Investigation of block shear of coped beams with welded clip angles

connection. MSc thesis, University of Macau, Macau, 2004.

35

Table 1 Cross-sectional dimensions of the test beams

Beam Designation

Beam Serial

tw (mm)

T (mm)

D (mm)

B (mm) Note

A, B (Beam406) UB406x140x46

6.8 11.2 403.2 142.4 Nominal 6.8 11.1 404.2 140.9 Measured

C, D (Beam457) UB457x191x74

9.1 14.5 457.0 190.4 Nominal 9.2 14.2 456.3 189.1 Measured

E (Beam356) UB356x171x67

9.1 15.7 363.4 173.2 Nominal 9.1 15.2 362.6 171.5 Measured

TB

twD

36

Table 2 Connection dimensions of the test specimens

Designation

Connected Length

ConnectionPosition

Cope Length

Cope Depth

Weld Size Note a

(mm) b

(mm) p

(mm) c

(mm) dc

(mm) s

(mm)

A1-406r3 50 160 20 100 30 8 Nominal 50 160 20 100 33 8.9 Measured

A2-406r2 70 140 20 120 30 8 Nominal 70 140 20 120 31 9.4 Measured

B1-406t 50 120 20 100 30 9 Nominal 50 120 20 100 30 10.0 Measured

B2-406r1 90 110 20 130 30 9 Nominal 90 110 20 130 30 9.9 Measured

C1-457R3 50 170 20 100 30 9 Nominal

50.5 170 20 99.5 30 11.2 Measured

C2-457T 50 120 20 100 30 11 Nominal 50 120 20.5 99 30 12.3 Measured

D1-457R1 90 120 20 150 30 11 Nominal 90 120 20 150 30 11.8 Measured

D2-457L 90 120 20 80 30 11 Nominal 90 120 20 80 30 12.6 Measured

E1-356T 50 120 20 100 30 11 Nominal 50 120 20 100 30 13.1 Measured

E2-356P 50 120 45 100 30 11 Nominal 50 120 45 100 30 13.5 Measured

c

dc

b b'

a

p

ss

37

Table 3 Summary of the test parameters

Test Parameter Specimen Designation Nominal Value

Aspect ratio (b'/a) A1-406r3, A2-406r2, B2-406r1 3.6, 2.3, 1.4 C1-457R3, D1-457R1 3.8, 1.6

Shear area, b (mm) C1-457R3, C2-457T 170, 120 Tension area, a (mm) C2-457T, D1-457R1 50, 90 Web thickness, tw (mm) B1-406t, C2-457T, E1-356T 6.8, 9.1, 9.1 Beam depth C2-457T, E1-356T UB457, UB356 Cope length, c (mm) D1-457R1, D2-457L 150, 80 Connection position, p (mm) E1-356T, E2-356P 20, 45

38

Coupon Specimen

Elastic Modulus

(MPa)

Static Yield, Fy

(MPa)

Static UltimateStrength, Fu

(MPa)

Final Elongation

(%) Beam406 (Beam A, B)

Flange 1 210476 308.3 439.9 21.8 Flange 2 211426 289.1 440.3 23.2 Average 210951 298.7 440.1 22.5 Web 1 182170 353.6 458.8 20.0 Web 2 199375 282.5 425.9 30.3 Average 190772 318.1 442.4 25.2

Beam457 (Beam C, D) Flange 1 215029 318.6 470.2 32.2 Flange 2 214906 329.8 469.5 31.0 Average 214967 324.2 469.9 31.6 Web 1 205786 372.7 487.9 32.4 Web 2 200683 370.5 487.4 26.6 Average 203234 371.6 487.7 29.5

Beam356 (Beam E) Flange 1 203706 297.1 433.3 28.9 Web 1 202210 305.0 444.4 19.7 Web 2 204720 303.1 443.8 18.3 Average 203465 304.1 444.1 19.0

Clip Angle Angle 1 201050 295.9 498.2 28.2 Angle 2 206292 314.9 499.6 29.6 Average 203671 305.4 498.9 28.9

Material properties according to EN 10025-2:2004

Steel Grade Elastic

Modulus(MPa)

Minimum Yield, Fy (MPa)

Tensile Strength, Fu

(MPa)

Minimum Percentage Elongation

(%) S275 210000 275 430 21 S355 210000 355 510 20

Table 4 Summary of the tension coupon test results

39

Table 5 Summary of the test results

Specimen Ultimate Load (kN)

Ultimate Reaction

(kN)

Connection Moment*

(kN.m)

Web Thickness Reduction+(%) Failure Mode

A1-406r3 483.8 395.2 -7.5 7.9 Buckling A2-406r2 531.5 437.4 -17.0 7.1 Buckling B1-406t 479.0 394.0 -14.8 5.9 Buckling B2-406r1 475.1 390.3 -13.3 4.9 Buckling C1-457R3 885.0 690.1 -4.8 5.6 Exceeded** C2-457T 804.9 630.0 -10.7 15.8 Fracture D1-457R1 795.1 623.0 -12.4 14.0 Buckling D2-457L 880.9 684.5 1.7 5.4 Exceeded** E1-356T 751.0 601.2 -8.6 15.3 Fracture E2-356P 725.4 581.0 -9.1 7.6 Buckling Note: * A negative moment indicates tension in the top flange. ** Failure did not take place at the maximum applied load. + Reduction in web thickness near the bottom of the clip angles.

40

Table 6 Summary of the predicted capacity and test capacity of the specimens

Specimen Failure Mode

Fy (MPa)

Fu (MPa)

Test Ultimate Reaction

CSA-S16-01 (2001)Eq. (2)

AISC LRFD (1999) Larger of Eq. (4) or

Eq. (5)

Eurocode 3 (1992) Eq. (6)

AIJ (1990) Lesser of Eq. (9) or

Eq. (10)

GB50017 (2003) Eq. (11)

PredictedCapacity

Test PredictedCapacity

Test PredictedCapacity

Test PredictedCapacity

Test PredictedCapacity

Test Predicted Predicted Predicted Predicted Predicted

A1-406r3 Buckling 318.1 442.4 395.2 336.8 1.17 472.7 0.84 341.5 1.16 417.8 0.95 510.5 0.77 A2-406r2 Buckling 318.1 442.4 437.4 341.0 1.28 479.9 0.91 351.3 1.25 453.0 0.97 535.9 0.82 B1-406t Buckling 318.1 442.4 394.0 284.9 1.38 400.5 0.98 291.5 1.35 367.8 1.07 441.0 0.89 B2-406r1 Buckling 318.1 442.4 390.3 332.1 1.18 482.5 0.81 348.5 1.12 459.5 0.85 544.0 0.72 D1-457R1 Buckling 371.6 487.7 623.0 540.6 1.15 769.4 0.81 564.2 1.10 742.5 0.84 851.4 0.73 E2-356P Buckling 304.1 444.1 581.0 422.8 1.37 606.0 0.96 431.4 1.35 539.0 1.08 669.9 0.87

Average 1.26 0.88 1.22 0.96 0.80 C2-457T Fracture 371.6 487.7 630.0 450.9 1.40 621.2 1.01 460.6 1.37 578.2 1.09 671.9 0.94 E1-356T Fracture 304.1 444.1 601.2 381.3 1.58 545.3 1.10 391.4 1.54 499.1 1.20 611.6 0.98

Average 1.49 1.06 1.45 1.15 0.96 C1-457R3 Exceeded 371.6 487.7 690.1 553.4 --- 755.8 --- 559.3 --- 676.9 --- 801.5 --- D2-457L Exceeded 371.6 487.7 684.5 540.6 --- 769.4 --- 564.2 --- 742.5 --- 851.4 ---

Note: All resistance factors are taken as 1.0. The units of forces are in kN.

41

Cope

Bolted connection Welded connection

Figure. 1 Schematic of a bolted or welded connection on a coped beam

42

Cope

Cope

Potential block of web material tearing off

Welded end connection

Potential block of web material tearing off

Bolted end connection

Figure. 2 Potential block shear failure in a coped beam

weld

Note: The block shear failure generally consists of shear yielding on the gross area of the shear face and tensile rupture along the net area of the tension face

Potential block shear failure mode

Potential block shear failure mode

43

Figure. 3 Block shear model of failure identified by Birkemoe and Gilmor (1978)

Rupture SurfaceB

B

A A

44

Figure 4 Block shear model proposed by Ricles and Yura (1983)

0.6Fy

Fu

45

c

dc

TB

twD

b b'

a

p

ss

Figure 5 Schematics of the test specimen

46

Note: All dimensions are in millimeters

Figure 6 Overall design dimensions of the test specimens

Beam E (UB 356x171x67)

356PE2

356TE1

Details of typical clip angle

26 Dia. holes for M24 bolt

Details of A1 clip angle

47

A1-406r3 A2-406r2 B1-406t B2-406r1

C1-457R3 C2-457T D1-457R1 D2-457L

E1-356T E2-356P

Note: All dimensions are in millimeters

Figure 7 Connection details of all of the test specimens

48

Figure 8 Schematic of the test setup

Test Beam

3300mm2700mm

Lateral BracingApplied Load (P)

Reaction (Q)

L

D

Support

Roller Assemblies

Load Cell (890kN)

Supporting Column

Test Beam

Hydraulic Cylinder (890 kN)

Bracing Column

Lateral Bracing

Test Frame

Concrete Strong Floor

Roller Assemblies Load Cell

(330kN)

Test Connection

Stub Support

Lateral Bracing

Beam L (mm) A 510 B 510 C 600 D 600 E 550

49

LVDT 3

LVDT 2 LVDT 1

LVDT 8 (lateral)

LVD

T 7LV

DT 6

LVDT 5

LVDT 4

Applied Load (P)

Reaction (Q)

Figure 9 Layout of LVDTs

50

Figure 10 Layout of strain gauges

20

19

24

141516

1 2 3 4 5 67

8 910

111213

2517

23

(Back side)18

26

Applied Load (P)

Reaction (Q)

51

(a) Specimen B2

(b) Specimen C1

(c) Specimen C2

(d) Specimen D1

52

(e) Specimen E1

Figure 11 Photos of failed specimens B2, C1, C2, D1, and E1

53

(a) Specimen A1

(b) Specimen B2

Figure 12 Photos of the buckled shapes of specimens A1 and B1

Top flange Beam web

buckled

Clip angle Bottom flange

54

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Deflection, δ (mm)

App

lied

Load

, P (k

N)

B1-406tA2-406r2

A1-406r3 B2-406r1

P

Figure 13 Applied load vs. load point deflection curves for specimens A1, A2, B1, and B2

55

Figure 14 Longitudinal strain distribution along the tension area for specimen E1

0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60 70 80 90 100 110 120

Distance from beam end (mm)St

rain

(mic

ro s

trai

n)

Test P=70kN

Test P=183kN

Wel

ded

Ang

le E

dge,

a=5

0mm

1 2 3 4 5Strain gauge #1

Strain gauge #5

56

0

20

40

60

80

100

120

140

160

180

0 500 1000 1500 2000

Strain (micro strain)

Dis

tanc

e fr

om to

p ed

ge o

f bea

m w

eb (m

m)

Test P=70kN

Test P=183kN

Figure 15 Shear strain distribution along the shear area for specimen E1

Clip angles

7 6

5

8 9 10

11 12 13

57

0

20

40

60

80

100

120

140

160

180

200

220

-1000 -900 -800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400

Strain (micro strain)

Dis

tanc

e fr

om to

p ed

ge o

f bea

m w

eb (m

m)

Test P=70kN

Test P=183kN

Figure 16 Flexural strain distribution along the shear area for specimen E1

7 6

5

8 9 10

11 12 13

58

Figure 17 Load vs. web deformation curves for specimens C1 and D1 (aspect ratio

series 2)

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7 8 9 10 11 12

Web Deformation, ∆1-∆2 (mm)

Con

nect

ion

Rea

ctio

n, Q

(kN

)

D1-457R1C1-457R3

Q

C1-457R3 D1-457R1

b’ b’

a a

b’/a = 1.6 b’/a = 3.8

100 150

59

Figure 18 Reaction versus web deformation curves for the shear area series

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7 8 9 10 11 12

Web Deformation, ∆1-∆2 (mm)

Con

nect

ion

Rea

ctio

n, Q

(kN

)

C2-457T

C1-457R3

Q

C1-457R3 C2-457T

100 100

60

Figure 19 Reaction versus web deformation curves for the web thickness and beam depth series

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8 9 10 11 12

Web Deformation, ∆1-∆2 (mm)

Con

nect

ion

Rea

ctio

n, Q

(kN

)

C2-457T

E1-356T

B1-406t (Modified)

Q

C2-457TB1-406t E1-356T

404

50

100 100

100

120 120

120

50 50

61

Figure 20 Reaction vs. web deformation curves for cope length series

0

100

200

300

400

500

600

700

800

0 1 2 3 4 5 6 7 8 9 10 11 12

Web Deformation, ∆1-∆2 (mm)

Con

nect

ion

Rea

ctio

n, Q

(kN

)

D1-457R1D2-457L Q

D1-457R1 D2-457L

120 120

90 90